I didn't find anything for this season, but the Edmonton Oilers took the most shots by a team in 2023-24, with 2,767 taken.

Interpreted as:

NHL 2023 or more shot team leaders this regular season

	TEAM	S	SEASON	GP	W	L	OTL	PTS	PTS%	SOW	SOL	G	GA	DIFF	PP%	PK%	S/GP	S%	SA/GP	SV%
1	Oilers	2,767	2023-24	82	49	27	6	104	.634	2	1	292	236	56	26.3	79.5	33.74	10.6	28.13	.898
2	Panthers	2,764	2023-24	82	52	24	6	110	.671	3	2	265	198	67	23.5	82.5	33.71	9.6	27.79	.913
3	Hurricanes	2,733	2023-24	82	52	23	7	111	.677	2	5	277	211	66	26.9	86.4	33.33	10.1	25.62	.900
4	Flyers	2,708	2023-24	82	38	33	11	87	.530	4	3	231	258	-27	12.2	83.4	33.02	8.5	27.13	.884
5	Avalanche	2,705	2023-24	82	50	25	7	107	.652	2	2	302	252	50	24.5	79.9	32.99	11.2	29.80	.897
6	Penguins	2,686	2023-24	82	38	32	12	88	.537	2	3	253	248	5	15.3	80.7	32.76	9.4	30.23	.900
7	Maple Leafs	2,673	2023-24	82	46	26	10	102	.622	5	2	298	261	37	23.9	76.9	32.60	11.1	29.84	.893
8	Predators	2,642	2023-24	82	47	30	5	99	.604	3	0	266	248	18	21.6	76.9	32.22	10.1	30.57	.901
9	Kings	2,616	2023-24	82	44	27	11	99	.604	2	5	254	210	44	22.6	84.6	31.90	9.7	28.00	.909
10	Senators	2,602	2023-24	82	37	41	4	78	.476	5	0	250	281	-31	18.0	75.1	31.73	9.6	29.66	.884
11	Stars	2,587	2023-24	82	52	21	9	113	.689	4	2	294	232	62	24.2	82.0	31.55	11.4	28.66	.901
12	Rangers	2,582	2023-24	82	55	23	4	114	.695	4	3	278	226	52	26.4	84.5	31.49	10.8	29.49	.907
13	Flames	2,572	2023-24	82	38	39	5	81	.494	0	4	253	267	-14	17.9	80.8	31.37	9.8	29.73	.890
14	Golden Knights	2,548	2023-24	82	45	29	8	98	.598	4	2	263	243	20	20.2	79.3	31.07	10.3	30.33	.902
15	Sabres	2,534	2023-24	82	39	37	6	84	.512	2	1	244	243	1	16.6	79.8	30.90	9.6	29.28	.899
16	Devils	2,516	2023-24	82	38	39	5	81	.494	0	2	264	281	-17	22.4	80.7	30.68	10.5	30.00	.886
17	Jets	2,488	2023-24	82	52	24	6	110	.671	0	1	259	198	61	18.8	77.1	30.34	10.4	29.62	.918
18	Wild	2,471	2023-24	82	39	33	10	88	.537	3	3	248	260	-12	22.7	74.5	30.13	10.0	29.72	.893
19	Islanders	2,470	2023-24	82	39	27	16	94	.573	1	5	245	258	-13	20.3	71.5	30.12	9.9	32.76	.904
20	Blue Jackets	2,458	2023-24	82	27	43	12	66	.402	3	2	234	298	-64	15.1	76.3	29.98	9.5	34.41	.894
21	Lightning	2,402	2023-24	82	45	29	8	98	.598	3	1	288	267	21	28.6	83.3	29.29	12.0	29.63	.890
22	Bruins	2,396	2023-24	82	47	20	15	109	.665	4	3	263	221	42	22.2	82.5	29.22	11.0	30.54	.912
23	Red Wings	2,375	2023-24	82	41	32	9	91	.555	3	1	275	273	2	23.1	79.6	28.96	11.6	32.40	.897
24	Blues	2,370	2023-24	82	43	33	6	92	.561	5	2	234	248	-14	18.0	78.6	28.90	9.9	32.13	.906
25	Kraken	2,347	2023-24	82	34	35	13	81	.494	3	4	214	232	-18	20.7	78.8	28.62	9.1	29.16	.903